Common reasons people want to give up their pets:
Behavior problems - If your cat has a behavior problem, you probably want to just give your problem to someone else but if you won't give this cat another chance, why should anyone else? Consider helping to fix the pet's problem before deciding it won't work for you. Most behavior problems aren't that hard to solve – but it will take time and effort to determine the cause. Remedies for some Common Behavior Problems

Allergies - It’s possible to develop an allergy at any point during your lifetime. You may suddenly find yourself sniffling and someone will mention, "maybe you are allergic to your cat". Most people only develope mild allergies and they can be easily controlled with the simple steps.

• Dander is what causes allergic reactions - keep it from collecting around the house by running the vacuum a few times a week.
• Allerpet/C Solution (see info link) for cats is a dander-reducing product that is very easy to apply. Simply wipe the animal down daily with a washcloth moistened with the liquid. Allergy sufferers swear by this product.
• Consider blinds that can be easily wiped down.
• Keep your cat out of your bedroom – create an 'allergy free' zone to sleep in.
• Steam-clean carpets a few times a year to remove allergens.
• Wash your hands after handling or playing with your pet.

We don't have enough time for the cat.
A cat really doesn't take that much time - his requirement for attention is less than you think. Will getting rid of your cat really make your life less stressful, or will getting him a playmate help?

We're moving-can't find a landlord who'll let us keep our pet.
Many landlords don't allow children either but would you give up up one of your kids? Affordable rental homes that allow pets are out there if you take the time to find them.

My new boyfriend doesn't like cats. Don't decide too quickly, your relationship with your cat may out last the human relationship.

If you decide that you really do have to give up your pet, PLEASE use this valuable guide offered by Best Friends Animal Society to find a safe new home -
How to find a home for pets